How long can I expect it will take to algebraically solve a system of $15$ nonlinear equations (without any numbers, only parameters), if I feed it into a computing software?
I'm asking for symbolic solving - is MAPLE, MATLAB, or Mathematica the best?
Here are the equations that I am talking about:
$$A - Ba - \frac{Va(c+d+t+s+h)}{z} - \frac{Wa(b+d)}{z} = 0$$
$$\frac{Wa(b+d)}{z} - \frac{Vb(c+d+t+s+h)}{z} - (B+D+GF)b = 0$$
$$\frac{Va(c+d+t+s+h)}{z} - \frac{Wc(b+d)}{z} - (B+E+C)c = 0$$
$$\frac{Vb(c+d+t+s+h)}{z} + \frac{Wc(b+d)}{z} - (B+C+D+F)d = 0$$
$$GFb - \frac{Ve(c+d+t+s+h)}{z} - (B+H)e = 0$$
$$He - \frac{Vf(c+d+t+s+h)}{z} - (B+S)f = 0$$
$$Sf - \frac{Vg(c+d+t+s+h)}{z}-Bg = 0$$
$$\frac{Vg(c+d+t+s+h)}{z} + Ss - (B+C+E)h = 0$$
$$Fd + \frac{Ve(c+d+t+s+h)}{z} - (B+C+H+T)t = 0$$
$$Ht + \frac{Vf(c+d+t+s+h)}{z} - (U+B+C+S+S)s = 0$$
$$Tt + \frac{W(b+d)x}{z} - (B+H+Y)u = 0$$
$$Us - (S+B)v + Hu - \frac{HvY}{H+S} = 0$$
$$S(s+v) - Bw + Zy+ Eh = 0$$
$$Ec - (\frac{W(b+d)}{z}+B)x = 0$$
$$Y(u + \frac{H}{H+S})v - (B+X)y- Zy = 0$$
WHERE:
$$z = a + b + c + d + e + f + g + h + s + t + u + v + w + x + y$$
AND:
$$ a,b,c,d,e,f,g,h,s,t,u,v,w,x,y,A,B,C,D,E,F,G,H,S,T,U,V,W,X,Y,Z > 0 $$
I hope someone can help, considering all the effort I have put in!! Thanks!